In recent years razors with various numbers of blades have been proposed in the patent literature e.g. in U.S. Pat. No. 5,787,586, which generally describes a razor with a handle and cartridge connected thereto and is herein incorporated by reference. More recently, the combination of a pivoting blade unit with a spring-biased biasing plunger has been demonstrated in US Patent App. No. 20050198841, herein incorporated by reference, and commercialized as the Fusion razor by The Gillette Company. This reactively tilting blade unit has provided further advantages in the field by providing a razor that adapts to contours of the surface of the body to improve the closeness and comfort of shaving. The biasing plunger may be secured using a stabilizing bore in the razor, the perimeter of which serves to prevent lateral motion of the biasing plunger and so prevent it appearing loose and the razor poorly made. However, it may be possible for the biasing plunger to stick or jam in the bore from which it protrudes which reduces the efficiency with which the razor conforms to the body's surface thus reducing the closeness and comfort of shaving. Accordingly, there remains a need for a razor offering improved reliability in the function of the pivoting blade unit.